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Proof step 398 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries2[str0], dirs) = dirs[entries2[str0]].nlink, dirs[m0] = mkdir(m1, md, # links(m0, dirs), m3, entries2), dirs[m] = mkdir(m2, md0, # links(m, dirs), m5, entries1), dirs[entries1[str]] = mkdir(m4, md4, # links(entries1[str], dirs), m7, ∅), dirs[entries2[str0]] = mkdir(dirs[entries2[str0]].size, md5, dirs[entries2[str0]].nlink, dirs[entries2[str0]].nsubdirs, entries0), entries1[str] ≠ ROOT_INO, afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, entries2[str0] ∈ dirs, entries1[str] ∈ dirs, str0 ∈ entries2, str ∈ entries1, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 399:
# links(entries2[str0], dirs) = m8, dirs[entries2[str0]] = mkdir(m6, md5, m8, m9, entries0), dirs[entries1[str]] = mkdir(m4, md4, # links(entries1[str], dirs), m7, ∅), dirs[m] = mkdir(m2, md0, # links(m, dirs), m5, entries1), dirs[m0] = mkdir(m1, md, # links(m0, dirs), m3, entries2), dirs[entries2[str0]] = mkdir(m6, md3, m8, m9, entries), afs-cons(dirs, files), str ∈ entries1, str0 ∈ entries2, entries1[str] ∈ dirs, entries2[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries1[str] = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[entries2[str0]], m6, md3, m8, m9, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[entries2[str0]], m6, md3, m8, m9, entries